Need Help With LSTM Neural Networks
(1) Yes this is the diagram for a classical LSTM unit. Of cause there are some variants and those diagrams would look slightly different.

(2) It is very common for researchers to use more than one layers of LSTM and achieves better performance than a single layer one. A common way to "stack" LSTMs is to use the previous layer's output ($h_t$ in your diagram) as the input to the next layer ($x_t$). However, I have seldom seen any successful application of 5+ layers of LSTMs, while for CNNs it is common to use tens or even hundreds of layers.